The Haar wavelet transform: its status and achievements

Relationship between Haar and Reed-Muller spectral and functional domains

“…Many other applications and achievements of ReedMuller transform in finding logic symmetries [7] as well as in error correcting codes [1] are also well known. The recent applications of Haar transform in logic design are described in [6]. The mutual relations between these two transforms are introduced here through recursive equations in the form of layered vertical and horizontal Kronecker products.…”

“…where I 2 n−1 is an identify matrix of 2 n−1 while the symbol "⊗" denotes Kronecker direct product [3,6]. Definition 2 The non-normalized Haar transform is obtained from replacing the nonzero entries of normalized Haar matrix with their arithmetic signs.…”

“…The non-normalized Haar transform preserves all the properties of the normalized Haar transform. Its matrix of order 2 n is defined as [3,6] …”

“…In this case it is also of interest to investigate mutual relations between various local discrete transforms such as, for example, Haar and Reed-Muller transform. Both Haar and Reed-Muller transforms have been used in many applications of logic design [2,3,6,7]. Therefore, it is not only interesting theoretically, but also practical to state their mutual relations.…”

Wavelet-Based Warping Technique for Mobile Devices

“…The power of wavelets is Multi-Resolution Analysis (MRA) which allows representing different levels of detail of images. The Haar wavelet [2] is one of the simplest wavelet transforms which can be used to transform large images into considerably smaller representations that then can be processed on mobile/ handheld devices at higher speeds. This paper proposes a framework to render novel views of compressed images using Haar wavelet based 3D warping technique on mobile devices.…”